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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals

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Freitas, Thiago H. [1] ; Jorge Perez, Victor H. [2]
Total Authors: 2
[1] Univ Tecnol Fed Parana, Campus Guarapuava, BR-85053525 Guarapuava - Brazil
[2] Univ Sao Paulo, ICMC, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: CZECHOSLOVAK MATHEMATICAL JOURNAL; v. 69, n. 2, p. 453-470, JUN 2019.
Web of Science Citations: 0

Let a, I, J be ideals of a Noetherian local ring (R,m,k). Let M and N be finitely generated R-modules. We give a generalized version of the Duality Theorem for Cohen-Macaulay rings using local cohomology defined by a pair of ideals. We study the behavior of the endomorphism rings of HI,Jt(M) and HI,Jt(M)), where t is the smallest integer such that the local cohomology with respect to a pair of ideals is nonzero and D(-):= Hom(R)(-, E-r(k)) is the Matlis dual functor. We show that if R is a d-dimensional complete Cohen-Macaulay ring and HI,Ji(R) = 0 for all i t, the natural homomorphism R Hom(r)(HI,Jt(K-R),HI,Jt(K-R)) is an isomorphism, where K-R denotes the canonical module of R. Also, we discuss the depth and Cohen-Macaulayness of the Matlis dual of the top local cohomology modules with respect to a pair of ideals. (AU)

FAPESP's process: 13/20723-7 - Finiteness properties and Artinianness of formal local cohomology modules dened by a PAIs of ideals
Grantee:Thiago Henrique de Freitas
Support type: Scholarships abroad - Research Internship - Doctorate
FAPESP's process: 12/01084-0 - Coefficients ideals for arbitrary ideals
Grantee:Thiago Henrique de Freitas
Support type: Scholarships in Brazil - Doctorate